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I'm curious to know what the drop rate of Black Lion Ticket Scraps from the Black Lion Chest.

If I was to open 100 BLC's how many scraps should I expect to receive?

It's linked in the 'Common drops' section of the wiki.

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There is a more or less hidden wiki article on the Black Lion Chest Drop rates, which is a user-curated list of drops, totalling 886 chests. Due to changes in the drop chances with patches, I would not trust on the reliability of this method.

A better way to check current droprates is to look on the Guild Wars 2 subreddit for posts of people mass-opening chests. According the most recent one documented on the Guild Wars 2 subreddit, there was an increase in drop chance after the then (April 1st, 2015) most recent patch.

Opening a total of 350 chests yielded 132 scraps and 7 full tickets, for an effective total of 202 scraps. This would place the effective droprate at around 57.7±4.1%. The error estimates here assumes that 350 is a big enough sample size for a Gaussian distribution (square root error).

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